In fluid mechanic measurements cameras are often used for recording a scene of small particles propagating in a fluid. In order to obtain 2D images a thin slice of the flow of particles is illuminated e.g. with a laser. The particle displacement between sequentially acquired images can then be analyzed using different techniques. It is necessary to calibrate the cameras to the illuminated plane, i.e. the millimeter to pixel ratio must be determined. Thereby distances travelled by the particles between consecutive images can be determined, and the velocity of the particles may be determined from the determined distances and the time elapsed between two successive images.
Several different techniques may be used for determining the velocity such as particle tracking velocimetry (PTV) if individual particle paths are followed or particle image velocimetry (PIV) if an average velocity for a cluster of neighboring particles is desired. For example, least squares matching algorithms or cross-correlation based algorithms may be used.
3D volume measurement methods also exist. In this case, a given volume of the flow of particles is illuminated instead of illuminating a thin slice of the flow. Two or more cameras are usually needed to detect the 3D particle positions in space and movements in time. A camera calibration is performed in order to estimate parameters of an imaging model that describe how positions in object space are mapped to the image plane of each camera. A calibration target having markers thereon of which the position is known is usually used for this calibration. In the context of the present application, such a calibration is considered a coarse or preliminary calibration.
After calibrating the cameras, the 3D position of particles may be estimated using known techniques.
However, the coarse or preliminary calibration is usually not accurate. With reference to FIG. 1, there is shown a particle 100 in an illuminated volume 102. Three cameras 104, 106 and 108 are used for capturing images of the particle 100 within the illuminated volume 102. The solid lines 110, 112 and 114 represent the mapping of the particle 100 onto the camera images 104, 106 and 108, respectively. The solid lines designated with reference numbers 115a, 115b and 115c illustrate the true, but unknown, position and orientation of the cameras 104, 106 and 108, while the dashed lines designated with reference numbers 116, 118 and 120 represent the assumed location and orientation of the cameras 104, 106 and 108 as described by the preliminary calibrations.
In this example, the orientation of the camera 104 is correct while its location is not; the location of the camera 106 is correct while its orientation is not; and both the position and orientation of the camera 108 are not correct.
The dashed lines 122, 124 and 126 represent the mapping of the particle 100 from the cameras 104, 106 and 108 back to the illuminated space. Since the calibration of the cameras 104, 106 and 108 is not accurate, i.e. the assumed position and/or orientation of the cameras 104, 106 and 108 is not correct, the lines 122, 124 and 126 do not intersect at the position of the particle 100. Instead the particle may be estimated to be located as shown by the dashed circle 128 (if a match is found at all). The results of this poor calibration can introduce undesirable errors in the data generated by the velocimetry system.
Based on the foregoing, there is a need for an improved method and system for calibrating a velocimetry system.